Question

Prove that lim(x->0) x^4cos(2/x)=0

Answer 1

use the old "squeeze theorem" since
\[-1\leq \cos(x)\leq 1\] and
\[\lim_{x\rightarrow 0}x^4=0\]

Answer 2

How do you know when to use the squeeze theorem? I just learned it recently and still have a bit of trouble with the concept.

Answer 3

i guess i don't have a good answer to that; i know it when i see it. but when you have a function like sine and cosine that is always bounded, you can often use it then. because sine and cosine can't ever by outside the interval [-1,1] if you want to show for example that
\[\lim_{x\rightarrow 0}x\sin(\frac{1}{x^2})=0\] you can use it

Answer 4

okay, thank you for your help!